English - British Curriculum - Year 10 & 11

(Ages 15-16)

Purpose of study

English has a pre-eminent place in education and in society. A high-quality education in

English will teach pupils to speak and write fluently so that they can communicate their

ideas and emotions to others and through their reading and listening, others can

communicate with them. Through reading in particular, pupils have a chance to develop

culturally, emotionally, intellectually, socially and spiritually. Literature, especially, plays a

key role in such development. Reading also enables pupils both to acquire knowledge

and to build on what they already know. All the skills of language are essential to

participating fully as a member of society; pupils, therefore, who do not learn to speak,

read and write fluently and confidently are effectively disenfranchised.

Aims

The overarching aim for English in the national curriculum is to promote high standards of

language and literacy by equipping pupils with a strong command of the spoken and

written word, and to develop their love of literature through widespread reading for

enjoyment. The national curriculum for English aims to ensure that all pupils:

- read easily, fluently and with good understanding

- develop the habit of reading widely and often, for both pleasure and information

- acquire a wide vocabulary, an understanding of grammar and knowledge of linguistic

conventions for reading, writing and spoken language

- appreciate our rich and varied literary heritage

- write clearly, accurately and coherently, adapting their language and style in and for a

range of contexts, purposes and audiences

- use discussion in order to learn; they should be able to elaborate and explain clearly

their understanding and ideas

- are competent in the arts of speaking and listening, making formal presentations,

demonstrating to others and participating in debate.

Spoken language

The national curriculum for English reflects the importance of spoken language in pupils’

development across the whole curriculum – cognitively, socially and linguistically. Spoken

language continues to underpin the development of pupils’ reading and writing during key

stage 4 and teachers should therefore ensure pupils’ confidence and competence in this

area continue to develop. Pupils should be taught to understand and use the conventions

for discussion and debate, as well as continuing to develop their skills in working

collaboratively with their peers to discuss reading, writing and speech across the

curriculum.

Reading and writing

Reading at key stage 4 should be wide, varied and challenging. Pupils should be

expected to read whole books, to read in depth and to read for pleasure and information.

Pupils should continue to develop their knowledge of and skills in writing, refining their

drafting skills and developing resilience to write at length. They should be taught to write

formal and academic essays as well as writing imaginatively. They should be taught to

write for a variety of purposes and audiences across a range of contexts. This requires

an increasingly wide knowledge of vocabulary and grammar.

Opportunities for teachers to enhance pupils’ vocabulary will arise naturally from their

reading and writing. Teachers should show pupils how to understand the relationships

between words, how to understand nuances in meaning, and how to develop their

understanding of, and ability to use, figurative language.

Pupils should be taught to control their speaking and writing consciously, understand why

sentences are constructed as they are and to use Standard English. They should

understand and use age-appropriate vocabulary, including linguistic and literary

terminology, for discussing their reading, writing and spoken language. This involves

consolidation, practice and discussion of language. It is important that pupils learn the

correct grammatical terms in English and that these terms are integrated within teaching.

Teachers should build on the knowledge and skills that pupils have been taught at key

stage 3. Decisions about progression should be based on the security of pupils’ linguistic

knowledge, skills and understanding and their readiness to progress to the next stage.

Pupils whose linguistic development is more advanced should be challenged through

being offered opportunities for increased breadth and depth in reading and writing. Those

who are less fluent should consolidate their knowledge, understanding and skills,

including through additional practice.

Reading

Pupils should be taught to:

- read and appreciate the depth and power of the English literary heritage through:

- reading a wide range of high-quality, challenging, classic literature and extended

literary non-fiction, such as essays, reviews and journalism. This writing should

include whole texts. The range will include:

- at least one play by Shakespeare

- works from the 19th, 20th and 21st centuries

- poetry since 1789, including representative Romantic poetry

- re-reading literature and other writing as a basis for making comparisons

- choosing and reading books independently for challenge, interest and

enjoyment.

- understand and critically evaluate texts through:

- reading in different ways for different purposes, summarising and synthesising

ideas and information, and evaluating their usefulness for particular purposes

- drawing on knowledge of the purpose, audience for and context of the writing,

including its social, historical and cultural context and the literary tradition to

which it belongs, to inform evaluation

- identifying and interpreting themes, ideas and information

- exploring aspects of plot, characterisation, events and settings, the relationships

between them and their effects

- seeking evidence in the text to support a point of view, including justifying

inferences with evidence

- distinguishing between statements that are supported by evidence and those

that are not, and identifying bias and misuse of evidence

- analysing a writer’s choice of vocabulary, form, grammatical and structural

features, and evaluating their effectiveness and impact

- making critical comparisons, referring to the contexts, themes, characterisation,

style and literary quality of texts, and drawing on knowledge and skills from

wider reading

- make an informed personal response, recognising that other responses to a text are

possible and evaluating these.

Writing

Pupils should be taught to:

- write accurately, fluently, effectively and at length for pleasure and information

through:

- adapting their writing for a wide range of purposes and audiences: to describe,

narrate, explain, instruct, give and respond to information, and argue

- selecting and organising ideas, facts and key points, and citing evidence, details

and quotation effectively and pertinently for support and emphasis

- selecting, and using judiciously, vocabulary, grammar, form, and structural and

organisational features, including rhetorical devices, to reflect audience, purpose

and context, and using Standard English where appropriate

- make notes, draft and write, including using information provided by others [e.g.

writing a letter from key points provided; drawing on and using information from a

presentation]

- revise, edit and proof-read through:

- reflecting on whether their draft achieves the intended impact

- restructuring their writing, and amending its grammar and vocabulary to improve

coherence, consistency, clarity and overall effectiveness

- paying attention to the accuracy and effectiveness of grammar, punctuation and

spelling.

Grammar and vocabulary

Pupils should be taught to:

- consolidate and build on their knowledge of grammar and vocabulary through:

- studying their effectiveness and impact in the texts they read

- drawing on new vocabulary and grammatical constructions from their reading

and listening, and using these consciously in their writing and speech to achieve

particular effects

- analysing some of the differences between spoken and written language,

including differences associated with formal and informal registers, and between

Standard English and other varieties of English

- using linguistic and literary terminology accurately and confidently in discussing

reading, writing and spoken language.

Spoken English

Pupils should be taught to:

- speak confidently, audibly and effectively, including through:

- using Standard English when the context and audience require it

- working effectively in groups of different sizes and taking on required roles,

including leading and managing discussions, involving others productively,

reviewing and summarising, and contributing to meeting goals/deadlines

- listening to and building on the contributions of others, asking questions to clarify

and inform, and challenging courteously when necessary

- planning for different purposes and audiences, including selecting and

organising information and ideas effectively and persuasively for formal spoken

presentations and debates

- listening and responding in a variety of different contexts, both formal and

informal, and evaluating content, viewpoints, evidence and aspects of

presentation

- improvising, rehearsing and performing play scripts and poetry in order to

generate language and discuss language use and meaning, using role,

intonation, tone, volume, mood, silence, stillness and action to add impact.

Maths - British Curriculum - Year 10 & 11

(Ages 15-16)

Purpose of study Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. Aims The national curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

- can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for key stage 4 is organised into apparently distinct domains, but pupils should develop and consolidate connections across mathematical ideas. They should build on learning from key stage 3 to further develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems.

They should also apply their mathematical knowledge wherever relevant in other subjects and in financial contexts. The expectation is that the majority of pupils will move through the programme of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

This programme of study specifies:

- the mathematical content that should be taught to all pupils, in standard type; and

- additional mathematical content to be taught to more highly attaining pupils, in bold type and braces { }.

Together, the mathematical content set out in the key stage 3 and key stage 4

programmes of study covers the full range of material contained in the GCSE

Mathematics qualification. Wherever it is appropriate, given pupils’ security of

understanding and readiness to progress, pupils should be taught the full content set out

in this programme of study.

Information and communication technology (ICT)

Calculators should not be used as a substitute for good written and mental arithmetic. In

secondary schools, teachers should use their judgement about when ICT tools should be

used.

Spoken language

The national curriculum for mathematics reflects the importance of spoken language in

pupils’ development across the whole curriculum – cognitively, socially and linguistically.

The quality and variety of language that pupils hear and speak are key factors in

developing their mathematical vocabulary and presenting a mathematical justification,

argument or proof. They must be assisted in making their thinking clear to themselves as

well as others and teachers should ensure that pupils build secure foundations by using

discussion to probe and remedy their misconceptions.

Schools are not required by law to teach the example content in [square brackets]

or the content indicated as being ‘non-statutory’.

Working mathematically

Through the mathematics content, pupils should be taught to:

Develop fluency

- consolidate their numerical and mathematical capability from key stage 3 and extend

their understanding of the number system to include powers, roots {and fractional

indices}

- select and use appropriate calculation strategies to solve increasingly complex

problems, including exact calculations involving multiples of π {and surds}, use of

standard form and application and interpretation of limits of accuracy

- consolidate their algebraic capability from key stage 3 and extend their understanding

of algebraic simplification and manipulation to include quadratic expressions, {and

expressions involving surds and algebraic fractions}

- extend fluency with expressions and equations from key stage 3, to include quadratic

equations, simultaneous equations and inequalities

- move freely between different numerical, algebraic, graphical and diagrammatic

representations, including of linear, quadratic, reciprocal, {exponential and

trigonometric} functions

- use mathematical language and properties precisely.

Reason mathematically

- extend and formalise their knowledge of ratio and proportion, including trigonometric

ratios, in working with measures and geometry, and in working with proportional

relations algebraically and graphically

- extend their ability to identify variables and express relations between variables

algebraically and graphically

- make and test conjectures about the generalisations that underlie patterns and

relationships; look for proofs or counter-examples; begin to use algebra to support

and construct arguments {and proofs}

- reason deductively in geometry, number and algebra, including using geometrical

constructions

- interpret when the structure of a numerical problem requires additive, multiplicative or

proportional reasoning

explore what can and cannot be inferred in statistical and probabilistic settings, and

express their arguments formally

- assess the validity of an argument and the accuracy of a given way of presenting

information.

Solve problems

- develop their mathematical knowledge, in part through solving problems and

evaluating the outcomes, including multi-step problems

- develop their use of formal mathematical knowledge to interpret and solve problems,

including in financial contexts

- make and use connections between different parts of mathematics to solve problems

- model situations mathematically and express the results using a range of formal

mathematical representations, reflecting on how their solutions may have been

affected by any modelling assumptions

- select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems; interpret their solution in the context of the given problem.

Number

In addition to consolidating subject content from key stage 3, pupils should be taught to:

- apply systematic listing strategies, {including use of the product rule for counting}

- {estimate powers and roots of any given positive number}

- calculate with roots, and with integer {and fractional} indices

- calculate exactly with fractions, {surds} and multiples of π; {simplify surd

expressions involving squares [for example 12 4 3 4 3 2 3 = ×= × =

×] and

rationalise denominators}

- calculate with numbers in standard form A 10n

, where 1 ≤ A < 10 and n is an integer

- {change recurring decimals into their corresponding fractions and vice versa}

- identify and work with fractions in ratio problems

- apply and interpret limits of accuracy when rounding or truncating, {including upper

and lower bounds}.

Algebra

In addition to consolidating subject content from key stage 3, pupils should be taught to:

• simplify and manipulate algebraic expressions (including those involving surds {and

algebraic fractions}) by:

- factorising quadratic expressions of the form 2 x bx c + +

2 ax bx c + +, including the

difference of two squares; {factorising quadratic expressions of the form}

- simplifying expressions involving sums, products and powers, including the laws

of indices

- know the difference between an equation and an identity; argue mathematically to

show algebraic expressions are equivalent, and use algebra to support and construct

arguments {and proofs}

- where appropriate, interpret simple expressions as functions with inputs and outputs;

{interpret the reverse process as the ‘inverse function’; interpret the succession

of two functions as a ‘composite function’}

- use the form y mx c = + to identify parallel {and perpendicular} lines; find the

equation of the line through two given points, or through one point with a given

gradient

- identify and interpret roots, intercepts and turning points of quadratic functions

graphically; deduce roots algebraically {and turning points by completing the

square}

- recognise, sketch and interpret graphs of linear functions, quadratic functions, simple

cubic functions, the reciprocal function 1

y = x

y x = cos with x ≠ 0, {the exponential function x y k = y x = sin

for positive values of k, and the trigonometric functions (with arguments

in degrees) , and y x = tan for angles of any size}

- {sketch translations and reflections of the graph of a given function}

- plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and

graphs of non-standard functions in real contexts, to find approximate solutions to

problems such as simple kinematic problems involving distance, speed and

acceleration

- {calculate or estimate gradients of graphs and areas under graphs (including

quadratic and other non-linear graphs), and interpret results in cases such as

distance-time graphs, velocity-time graphs and graphs in financial contexts}

- {recognise and use the equation of a circle with centre at the origin; find the

equation of a tangent to a circle at a given point}

- solve quadratic equations {including those that require rearrangement}

algebraically by factorising, {by completing the square and by using the quadratic

formula}; find approximate solutions using a graph

- solve two simultaneous equations in two variables (linear/linear {or linear/quadratic})

algebraically; find approximate solutions using a graph

- {find approximate solutions to equations numerically using iteration}

- translate simple situations or procedures into algebraic expressions or formulae;

derive an equation (or two simultaneous equations), solve the equation(s) and

interpret the solution

- solve linear inequalities in one {or two} variable{s}, {and quadratic inequalities in

one variable}; represent the solution set on a number line, {using set notation and

on a graph}

- recognise and use sequences of triangular, square and cube numbers, simple

aritmetic progressions, Fibonacci type sequences, quadratic sequences, and simple

geometric progressions (r n where n is an integer, and r is a positive rational

number {or a surd}) {and other sequences}

- deduce expressions to calculate the nth term of linear {and quadratic} sequences.

Ratio, proportion and rates of change

In addition to consolidating subject content from key stage 3, pupils should be taught to:

- compare lengths, areas and volumes using ratio notation and/or scale factors; make

links to similarity (including trigonometric ratios)

- convert between related compound units (speed, rates of pay, prices, density,

pressure) in numerical and algebraic contexts

- understand that X is inversely proportional to Y is equivalent to X is proportional to 1

Y ;

{construct and} interpret equations that describe direct and inverse proportion

- interpret the gradient of a straight line graph as a rate of change; recognise and

interpret graphs that illustrate direct and inverse proportion

- {interpret the gradient at a point on a curve as the instantaneous rate of change;

apply the concepts of instantaneous and average rate of change (gradients of

tangents and chords) in numerical, algebraic and graphical contexts}

- set up, solve and interpret the answers in growth and decay problems, including

compound interest {and work with general iterative processes}.

Geometry and measures

In addition to consolidating subject content from key stage 3, pupils should be taught to:

- interpret and use fractional {and negative} scale factors for enlargements

- {describe the changes and invariance achieved by combinations of rotations,

reflections and translations}

- identify and apply circle definitions and properties, including: centre, radius, chord,

diameter, circumference, tangent, arc, sector and segment

- {apply and prove the standard circle theorems concerning angles, radii,

tangents and chords, and use them to prove related results}

- construct and interpret plans and elevations of 3D shapes

- interpret and use bearings

- calculate arc lengths, angles and areas of sectors of circles

- calculate surface areas and volumes of spheres, pyramids, cones and composite

solids

- apply the concepts of congruence and similarity, including the relationships between

lengths, {areas and volumes} in similar figures

- apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in

right-angled triangles {and, where possible, general triangles} in two {and three}

dimensional figures

- know the exact values of sin cos θ θ and

0 0 0 θ = 0 , 30 , 45 60 0 and

sin sin sin

abc

ABC = =

for 0 0 0 0 θ = 0 , 30 , 45 , 60 90 0 and ; know the

exact value of tanθ

a2 = b2 2 + − c 2bc cos A

1 Area = sin

2

ab C

for

- {know and apply the sine rule, , and cosine rule,

, to find unknown lengths and angles}

- {know and apply to calculate the area, sides or angles of any

triangle}

describe translations as 2D vectors

- apply addition and subtraction of vectors, multiplication of vectors by a scalar, and

diagrammatic and column representations of vectors; {use vectors to construct

geometric arguments and proofs}.

Probability

In addition to consolidating subject content from key stage 3, pupils should be taught to:

- apply the property that the probabilities of an exhaustive set of mutually exclusive

events sum to one

- use a probability model to predict the outcomes of future experiments; understand

that empirical unbiased samples tend towards theoretical probability distributions, with

increasing sample size

- calculate the probability of independent and dependent combined events, including

using tree diagrams and other representations, and know the underlying assumptions

- {calculate and interpret conditional probabilities through representation using

expected frequencies with two-way tables, tree diagrams and Venn diagrams}.

Statistics

In addition to consolidating subject content from key stage 3, pupils should be taught to:

- infer properties of populations or distributions from a sample, whilst knowing the

limitations of sampling

- interpret and construct tables and line graphs for time series data

- {construct and interpret diagrams for grouped discrete data and continuous

data, i.e. histograms with equal and unequal class intervals and cumulative

frequency graphs, and know their appropriate use}

- interpret, analyse and compare the distributions of data sets from univariate empirical

distributions through:

- appropriate graphical representation involving discrete, continuous and

grouped data, {including box plots}

- appropriate measures of central tendency (including modal class) and spread

{including quartiles and inter-quartile range}

- apply statistics to describe a population

- use and interpret scatter graphs of bivariate data; recognise correlation and know that

it does not indicate causation; draw estimated lines of best fit; make predictions;

interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.